"crossfire by" is correct and can be used in written English.
The phrase can be used to describe a situation in which one person is caught in the middle of an argument or dispute between two other people or groups. For example, "The mayor was caught in the crossfire by the two opposing sides of the debate."
Ms. Shahar's e-mail said: "To us, this photograph epitomizes everything tragic about the present violence: Children led into the crossfire by their own parents for publicity purposes.
Stevie Ray Vaughan: Caught in the Crossfire by Joe Nick Patoski and Bill Crawford.
She escaped from the crossfire by crossing ahead of San Francisco and passing to the disengaged side of Scott's column.
For three hours the battalion fought, pinned in a crossfire by North Korean soldiers on higher ground.
However, he had made a serious misjudgement: he had left enough room between Guerrier and the shoals for an enemy ship to cut across the head of the French line and proceed between the shoals and the French ships, allowing the unsupported vanguard to be caught in a crossfire by two divisions of enemy ships.
Now, Newt Gingrich ending an episode of "Crossfire" by belting out a stirring rendition of "I Love Trash"?
"If they stay inside Mosul, they risk being killed by heavy weapons and used as human shields by Isis, or being caught in crossfire, shot by snipers or stepping on landmines if they try to flee.
Since September 2012 she has been caught up in partisan crossfire, accused by Republicans of misleading the American public by delivering a false account of deadly attacks on American missions in the Libyan city of Benghazi.
But human rights advocates have said that the bulk of the casualties are probably civilians — killed in bombardments, caught in crossfire, hit by snipers or massacred in what many call an increasingly sectarian battle.
With all of the crossfire caused by former Rep. Harold Ford's debate about entering the Senate race against Gillibrand, the White House's heavy hand is on display yet again.
Six were killed by crossfire or shrapnel during the battle and three by artillery fire just before midnight.
